Posted by Yon Bard on July 03, 1999 at 21:04:25:
In Reply to: Re: Interpretation of C14 results posted by Henry Sadovsky on July 03, 1999 at 18:12:41:
:
: Dear Mr. Bard,
: Your thought experiment is nothing more than the "proof" of a tautology. That is, if a piece was created in 1800, it is not 17th c. Can't argue with that.
That is correct. I was merely pointing out that you shouldn't take this result as evidence that the piece probably dates from the 16th century, which as I painstakingly try to explain, it is not. I obviously failed, since you still appear to take it as such.
: Of course if we know that a piece was created in 1800, the C14 data adds no useful info. Why in the world bother to have even obtained the study (other than to test the performance of a laboratory)?
I was only using this as a simple illustration, leading on to the less straightforward cases.
: You point out that "Taking, for example, the Salor chuval fragment from the bottom of page 82, we are told that with 95% confidence, the piece has a 74.6% probability of dating from 1485-1608, and an 18% probability of dating from 1742-1808." Using the C14 data alone, on the sample submitted and prepared and analyzed by the Zurich lab, that is exactly what we may conclude. If you had no further information on the age of the piece, would you bet $10,000, with even odds, that it was 17th or 18th c.?
I am not a betting man. However, I challenge you to explain the meaning of the passage in double quotes. What exactly does it mean to you that a given rug was made between such and such dates with such and such a probability? I submit that the statement is meaningless unless we define the population of rugs that we are dealing with. And unless the population is the one I describe (i.e., with the uniform distribution) the stated results are simply wrong. And since it is reasonable to suppose that extant Salor chuvals do not have that distribution, it follows that the quoted probabilities do not apply.
: Of course, if we have an independent assesment of age prior to performing C14 analysis, this will need to be taken into account when interpreting the data. Do you have any such independent information on when the Salor chuval fragment was created?
That is a good question. There is a school of thought in statistical inference which admits 'informed opinion' as a basis for generating a prior distribution, and tells us how these opinions are modified in light of the results of the experiment. But no matter how disdainful we are of 'informed opinion', the fact remains, as stated above, that if you accept the cited probabilities, you are tacitly accepting the uniform distribution as your 'informed opinion'. There is simply no way of avoiding making some a-priori assumptions about the distribution of ages.
: I am not endorsing the C14 method for the dating of this chuval but simply clarifying an analysis that seems to me to obfuscate the issue.
If pointing out that the original analysis is inapplicable in practice and describing the parameters within which it might be valid is 'obfuscation' then I plead guilty.
Regards, Yon
: Good rugs to you,
: Henry Sadovsky